Recently, there has been great interest in multiple input and multiple output (MIMO) systems, which use multiple antennas on both a transmitter side and a receiver side of a communication system to improve communication performance. The MIMO technique has been employed in a variety of communication systems and is included in IEEE standards 802.11 and 802.16. There is, therefore, a need for increasing the performance of MIMO systems.
Improving spatial diversity gain may provide improved communication performance in a MIMO system. For example, when data signals including the same data are respectively transmitted by the multiple transmitting antennas of the MIMO system, spatial diversity results. With the data signals transmitted over multiple spatially separated communications channels, loss of signal due to fade or inference may be reduced, and data signals respectively received by the multiple receiving antennas of the MIMO system may be constructively combined to retrieve the data. In other words, the MIMO system has spatial diversity gain.
Because there are multiple transmitting antennas and multiple receiving antennas in the MIMO system, a communication channel is established between each of the transmitting antennas and each of the receiving antennas. A channel matrix H may be used to represent the communication channels between the transmitting antennas and the receiving antennas. Each element hi,j in the channel matrix H denotes a channel gain of a communication channel between a jth one of the transmitting antennas and an ith one of the receiving antennas. Typically, the channel gain hi,j is a complex number having a magnitude and a phase. For example, for a signal at a certain frequency propagating through the communication channel having the channel gain hi,j, the magnitude of the channel gain hi,j indicates how much the signal would be amplified or attenuated, and the phase of the channel gain hi,j indicates how much a phase of the signal would be changed.
An example method to increase the spatial diversity gain of the MIMO system is to determine a phase of each of the multiple transmitting antennas of the MIMO system, based on singular value decomposition (SVD) of the channel matrix H, where the SVD is a matrix factorization method in the art of linear algebra. However, in reality, each of the multiple transmitting antennas of the MIMO system may have a transmitting power constraint. In other words, the MIMO system may have per-antenna transmitting power constraints. When the SVD-based method is used to determine a phase of each of the transmitting antennas of the MIMO system that has per-antenna transmitting power constraints, the determined phase of each of the transmitting antennas may degrade performance of the MIMO system.